Sovereign debt maths show risk of vicious circle

How can a country support debt of over 100 percent of GDP for many years and then suddenly start spiralling towards insolvency? That question of sovereign debt maths is not merely academic. It is highly relevant to the likes of Greece and Italy.

The answer is that size of the sovereign debt burden is not everything when it comes to keeping up with interest payments. No matter how high the ratio of debt to GDP may be, it does not need to increase as long as the government has two factors going its way: the “primary” budget balance — the balance before interest payments — and the growth rate of nominal GDP.

To see how these play out, consider two countries. One has a moderate debt load, 50 percent of GDP, which carries a 4 percent average interest rate. If the budget is in primary balance, the government will still run a deficit of 2 percent of GDP, which is 4 percent (the interest rate) of 50 percent (the debt). As long as nominal GDP grows by 4 percent, the ratio of debt to GDP stays the same.

The other country is highly indebted, with a debt/GDP ratio of 100 percent. Assume it also pays an interest rate of 4 percent. With a primary budget balance, its fiscal deficit is 4 percent of GDP. However, as long as nominal GDP keeps growing at 4 percent a year, the ratio of debt to GDP stays the same — 100 percent.

In effect, the highly-indebted government doesn’t pay a penalty for its profligacy, as long as growth keeps up and interest rates stay low. Greece and other heavily indebted countries benefited from such a happy environment for years.

But the equilibrium is fragile. It can be disturbed in three ways: nominal GDP growth can decline, interest rates can go up or the country can start running a primary deficit. The pain is much worse for highly indebted countries like Greece, which has managed all three at once.

Start with growth. Imagine nominal GDP growth drops to zero. If nothing is done, the debt/GDP ratio will rise by 2 percentage points in the moderately indebted country, but by 4 percentage points in the highly indebted one.

Countries can keep that key ratio from increasing, by running compensating primary surpluses. That means moving from balance to a surplus of 2 percent of GDP for the moderately indebted and from zero to 4 percent for the heavily indebted. The higher the debt level, the more the government’s belt will have to be tightened.

But such budgetary squeezes tend to put further downward pressure on GDP — making the debt burden even heavier. Imagine that actual GDP falls by a quarter of a percentage point for every budget surplus increase of one percentage point of GDP. The 4 percent fiscal squeeze would then knock GDP by one percent in the profligate country, while the modestly indebted country’s GDP would fall half a percent.

Next, interest rates. Investors jack up interest rates to compensate for the risk that the population will not stomach a humungous budget squeeze. Foreign buyers are likely to be more demanding than patriotic domestic ones. As the proportion of expensive debt increases, the government’s interest bill rises, potentially starting a debt snowball.

Finally, the government’s budget. While the state would ideally be aiming for a budget surplus, recessions normally lead to higher deficits. As business activity drops off, tax revenue falls and more people qualify for government benefits. This is the worst moment for markets to turn hostile.

When all three factors — economic contraction, higher rates and rising deficits — come at once, they easily start fuelling one another in a vicious cycle. If the profligate country has to pay a 6 percent interest rate instead of 4 percent and recession and belt-tightening have cut nominal GDP by 2 percent, a primary surplus of just over 8 percent is required just to keep the ratio of debt to GDP stable.

That is a huge move, and may be too much to bear politically for the sort of country which has historically run big deficits. Investors have good reason to fear some sort of debt work-out. They then don’t push up the interest rate they are prepared to lend at — they stop lending completely.

You left out one big factor – the balance of trade. Running a large trade deficit robs the economy of jobs and forces the government to rely more heavily on deficit spending to prop up social safety net programs.

Greece has the highest per capita trade deficit of any developed nation, more than double that of the U.S.